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    "氢原子光谱指的是氢原子内之电子在不同能级跃迁时所发射或吸收不同波长、能量之光子而得到的光谱。氢原子光谱为不连续的线光谱，自无线电波、微波、红外光、可见光、到紫外光区段都有可能有其谱线。根据电子跃迁的后所处的能阶，可将光谱分为不同的线系。理论上有无穷个线系，前6个常用线系以发现者的名字命名。 [1]"
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    "# 氢原子光谱计算公式\n",
    "\n",
    "## 1. 核心公式：里德伯公式 (Rydberg Formula)\n",
    "\n",
    "氢原子发射或吸收光谱的波数 ($\\tilde{\\nu}$)、波长 ($\\lambda$) 或频率 ($\\nu$) 由以下公式计算：\n",
    "\n",
    "### 波数形式（最常用）\n",
    "$$\n",
    "\\tilde{\\nu} = \\frac{1}{\\lambda} = R_H \\left( \\frac{1}{n_1^2} - \\frac{1}{n_2^2} \\right)\n",
    "$$\n",
    "\n",
    "### 波长形式\n",
    "$$\n",
    "\\lambda = \\frac{1}{R_H \\left( \\frac{1}{n_1^2} - \\frac{1}{n_2^2} \\right)}\n",
    "$$\n",
    "\n",
    "### 频率形式\n",
    "$$\n",
    "\\nu = c \\cdot R_H \\left( \\frac{1}{n_1^2} - \\frac{1}{n_2^2} \\right)\n",
    "$$\n",
    "\n",
    "## 2. 参数说明\n",
    "\n",
    "| 符号 | 含义 | 数值/要求 |\n",
    "|------|------|-----------|\n",
    "| $\\tilde{\\nu}$ | 波数 (Wavenumber) | 单位：$\\mathrm{cm}^{-1}$ 或 $\\mathrm{m}^{-1}$ |\n",
    "| $\\lambda$ | 波长 (Wavelength) | 单位：m |\n",
    "| $\\nu$ | 频率 (Frequency) | 单位：Hz |\n",
    "| $R_H$ | 氢的里德伯常数 | $10967758.1 \\ \\mathrm{m}^{-1}$ (计算可取 $1.097 \\times 10^7 \\ \\mathrm{m}^{-1}$) |\n",
    "| $c$ | 真空光速 | $2.99792458 \\times 10^8 \\ \\mathrm{m/s}$ |\n",
    "| $n_1, n_2$ | 主量子数 | 正整数，且 $n_2 > n_1$ |\n",
    "\n",
    "## 3. 光谱线系分类\n",
    "\n",
    "根据 $n_1$ 的取值，氢原子光谱分为以下线系：\n",
    "\n",
    "| 线系名称 | $n_1$ | $n_2$ | 光谱区域 |\n",
    "|----------|-------|-------|----------|\n",
    "| **莱曼系** (Lyman series) | 1 | 2, 3, 4, ... | 紫外区 |\n",
    "| **巴耳末系** (Balmer series) | 2 | 3, 4, 5, ... | 可见光区（部分） |\n",
    "| **帕邢系** (Paschen series) | 3 | 4, 5, 6, ... | 红外区 |\n",
    "| **布拉克系** (Brackett series) | 4 | 5, 6, 7, ... | 红外区 |\n",
    "| **普丰德系** (Pfund series) | 5 | 6, 7, 8, ... | 红外区 |\n",
    "\n",
    "## 4. 能量形式表示\n",
    "\n",
    "### 能级公式\n",
    "$$\n",
    "E_n = -\\frac{13.6}{n^2} \\ \\text{eV}\n",
    "$$\n",
    "\n",
    "### 跃迁能量公式\n",
    "$$\n",
    "\\Delta E = E_2 - E_1 = 13.6 \\left( \\frac{1}{n_1^2} - \\frac{1}{n_2^2} \\right) \\ \\text{eV}\n",
    "$$\n",
    "\n",
    "### 光子能量关系\n",
    "$$\n",
    "E = h\\nu = \\frac{hc}{\\lambda}\n",
    "$$\n",
    "\n",
    "## 5. 计算示例\n",
    "\n",
    "**计算巴耳末系 H-α 线（$n_2=3 \\rightarrow n_1=2$）的波长：**\n",
    "\n",
    "$$\n",
    "\\frac{1}{\\lambda} = R_H \\left( \\frac{1}{2^2} - \\frac{1}{3^2} \\right) = 1.097 \\times 10^7 \\left( \\frac{1}{4} - \\frac{1}{9} \\right)\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\frac{1}{\\lambda} = 1.097 \\times 10^7 \\times \\frac{5}{36} \\approx 1.5236 \\times 10^6 \\ \\mathrm{m}^{-1}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\lambda \\approx \\frac{1}{1.5236 \\times 10^6} \\approx 6.563 \\times 10^{-7} \\ \\mathrm{m} = 656.3 \\ \\mathrm{nm}\n",
    "$$\n",
    "\n",
    "**计算结果：** 656.3 nm（红色可见光）"
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